There are effectively 5 mobile phone providers: CSL (using three brands: 1O1O, one2Free, NewWorld), PCCW Mobile, Smartone-Vodafone, Peoples-China Mobile, 3 (Hutchison). All of them have sizeable market shares, but none is dominant.
For voice and SMS (which is all I use) I am currently with CSL one2Free, having previously been with 1O1O, 3, and PCCW Mobile at various points through my 10+ years here. I found PCCW Mobile's SMS service to be unreliable so I would not recommend them. CSL seems to be generally regarded as having the best network coverage, and I am happy with them (albeit that they have a dodgy period a while back whilst they did a major network equipment change out).
As to plans, the key thing is to get a plan which you are sure has enough minutes bundled in for what you need. Minutes above the plan commitment are relatively expensive. For SMS the pricing is much the same, but if there is one number that you will SMS a lot (for example your partner) then you should both be on the same network since intra-network SMSs are generally free (up to some limit at least, and very cheap thereafter).
The exact plans change all the time, and all involve commitment periods. Note that you can change your plan upwards during the commitment period, but not, generally, downwards. As a benchmark, my plan with one2Free costs me $59 (nominally $69 less $10 for doing credit card autopay) for 600 basic minutes of airtime per month. I end up spending almost as much on SMS (at $0.8 inter-network, $1.5 international)
You should buy international calls separately from your mobile plan. Personally I use IDT1529 primarily, but I also have backup accounts with 0060 and 0080; there are many others to choose from. There is no generally subscription charge for IDD so it's just pay as you go. However, if you consistently make a lot of calls to certain destinations then you may save a little by buying a fixed price "all you can eat" subscription such as 0088. Note however, that these deals only cover routes which are generally very cheap anyway, and you normally have to commit to paying the monthly rate for 12 months or more, so I wouldn't recommend them until you have been here a while and seen what your calling patterns are like.